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1.	Brandes, Julia, 1986, et al. (author) ON THE INHOMOGENEOUS VINOGRADOV SYSTEM 2022 In: Bulletin of the Australian Mathematical Society. - 1755-1633 .- 0004-9727. ; 106:3, s. 396-403 Journal article (peer-reviewed)abstract We show that the system of equations Sigma(s)(i=1)(x(i)(j) - y(i)(j)) = a(j) (1 <= j <= k) has appreciably fewer solutions in the subcritical range s < 1/2k(k + 1) than its homogeneous counterpart, provided that al not equal 0 for some l <= k - 1. Our methods use Vinogradov's mean value theorem in combination with a shifting argument.
2.	Brandes, Julia, et al. (author) ON THE INHOMOGENEOUS VINOGRADOV SYSTEM 2022 In: Bulletin of the Australian Mathematical Society. - : Cambridge University Press (CUP). - 0004-9727 .- 1755-1633. ; 106:3, s. 396-403 Journal article (peer-reviewed)abstract We show that the system of equations Sigma(s)(i=1)(x(i)(j) - y(i)(j)) = a(j) (1 <= j <= k) has appreciably fewer solutions in the subcritical range s < 1/2k(k + 1) than its homogeneous counterpart, provided that al not equal 0 for some l <= k - 1. Our methods use Vinogradov's mean value theorem in combination with a shifting argument.

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Author/Editor: Hughes, K. (1); Brandes, Julia, 1986 (1); Brandes, Julia (1); Hughes, Kevin (1)

University: University of Gothenburg (1); Chalmers University of Technology (1)

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